Panes with Horizontal Prismatic Ribs
Panes with horizontal prismatic ribs for vertical windows which are directed to the south and which reject or transmit direct solar radiation depending on the actual solar elevation angle are known since 1980 (French patent application no. 8017364, publication no. 2463254). Adequate dimensioning of the cross-section of the rib (FIG. 1) causes the refraction of rays when penetrating the upper surface of the ribs and then--in case--the total internal reflection of rays at the rear surface of the pane in such a way that the direct solar radiation is rejected in summer and transmitted in winter. The basic prism angle .theta. is determined such that the equation
sin(.eta..sub.G -.theta.)=n.multidot.sin(.kappa.-.theta.) (1)
with n: the refractive index of the pane material which is about 1.5 for common mon window glass and for acrylic glass,
.eta..sub.G : the chosen limiting value of the solar elevation angle .eta..sub.S at 12 o'clock local time--i.e. the solar rays impinging at an angle .eta..sub.S &lt;.eta..sub.G are to be rejected and those impinging at an angle .eta..sub.S &lt;.eta..sub.G are to be transmitted--and PA1 .kappa.=arcsin(1/n), the critical angle of total reflection, PA1 with .lambda.: the geographical latitude of the application site. PA1 .delta.: the angle of solar declination relative to the equator, PA1 .delta..sub.0 =23.45.degree., the maximum angle of solar declination relative to the equator at the annual time of summer solstice, PA1 d.sub.J =365.25 days, the period of a year, EQU .beta..sub.v =-arctan(tan.DELTA..beta./sin.lambda.), (4) PA1 t: the mean local daytime, PA1 .beta.=.pi./12h.multidot.t: the daytime angle, EQU .eta..sub.0 =-arcsin(cos.beta..sub.v.multidot.cos.lambda.cos.alpha.), (5) PA1 with sin.eta..sub.1 =1/n.multidot.sin.eta., if the radiation is parallel incident to the cross-sectional plane.
holds. If the window with the prismatic pane is directed to the south, the vector of solar radiation at the local time t.sub.v =12 o'clock is located within the cross-sectional planes of the ribs, is perpendicular to the longitudinal axes of the ribs and the horizontal prismatic ribs are parallel to the equator plane. Therefore, the direction of the prismatic pane to the south has the consequence that the functional dependency on local time of the incident angle .gamma..sub.2 of the rays impinging on the rear surface of the pane--.gamma..sub.2 being decisive for reflection or transmission--is symmetrical to the local time t.sub.v =12 o'clock. For radiation which is irradiated with identical incident angles from the clear or the overcast sky this reflective property of the prismatic ribs is, of course, the same as for radiation incident from the sun. In summer time, therefore, the room temperatures remain in acceptable limits, whereas in winter time the energy of solar radiation contributes to the reduction of heating energy. However, this prismatic pane offers no clear view and is applicable for vertical windows only which are essentially directed to the south. In comparison to common glass panes this prismatic pane offers a better protection from glare of direct solar radiation at locations in the vicinity of a window, but does not achieve an improved daylighting of the deeper parts of a room.
Panes with Non-Horizontal Prismatic Ribs
A later development (European patent application no. 97113294.9-2205) describes, how panes with prismatic ribs may achieve this performance for all vertical windows with a direction between southeast by east and southwest by west. This is accomplished by prismatic ribs which are declined--depending on the deviation .DELTA..beta. of the window direction from the south--by a certain angle .alpha. to the horizontal plane. The angle .alpha. is determined by the EQU tan.alpha.=-sin.DELTA..beta./tan.lambda. (2)
For a variety of window directions the declination of the prismatic ribs relative to the horizontal plane is presented in FIG. 2. The angle .eta. is generally defined as the angle between the directional component of a ray within the cross-sectional plane of the rib and the intersecting straight line between the horizontal plane and the cross-sectional plane of the rib. The limiting angle .eta..sub.G between the vector of solar radiation and the intersecting straight line between the horizontal plane and the cross-sectional plane of the rib is determined for the daytime angle .beta..sub.v with the aid of the equations EQU .delta..sub.G =.delta..sub.0.multidot.cos(2.pi..multidot.d.sub.G /d.sub.J), (3)
the limiting angle of the solar declination relative to the equator plane at the times of the year, when there is just no solar radiation to be transmitted anymore or, respectively, when there is just solar radiation to be transmitted again by the prismatic pane, with
the daytime angle at which the vector of solar radiation is within the cross-sectional planes of the ribs and is perpendicular to the longitudinal axes of the ribs, with
the angle between the vector of solar radiation and the intersecting straight line between the horizontal plane and the cross-sectional plane of the rib for the daytime angle .beta..sub.v and the solar declination angle .delta.=0.degree. and EQU .eta..sub.G =.delta..sub.G +.eta..sub.0. (6)
The basic prism angle .theta. is calculated from the equation EQU tan.theta.=(1-sin.eta..sub.G)/[(n.sup.2 -1).sup.1/2 -cos.eta..sub.G ]. (7)
Eqn. 7 is an explicit form of eqn. 1. The maximum possible angle .eta. between the vector of solar radiation and the intersecting straight line between the horizontal plane and the cross-sectional plane of the rib for daytime angle .beta..sub.v at the annual time of summer solstice is EQU .eta..sub.M =.delta..sub.0 +.eta..sub.0. (8)
The angle .OMEGA. of the cross-section of the ribs is determined such that EQU .OMEGA..gtoreq..pi./2-.eta..sub.G (9)
holds. If EQU .OMEGA..gtoreq..pi./2-.theta.-arcsin[sin(.eta..sub.M -.eta.)/n]
is valid, which is true for great deviations of the window direction from the south and/or great solar radiation blockade periods, a saw tooth profile with specific angles is provided for the lower faces of the prismatic ribs (FIG. 3). For a correspondingly dimensioned prismatic pane the functional dependence on daytime of the solar incident angle .gamma..sub.2 at the rear face of the prismatic pane which is decisive for reflection or transmission is symmetrical to the daytime t.sub.v, has a minimum at this daytime and the level of the angle values increases with the annual time approaching summer solstice. This functional dependence on daytime of the solar incident angle .gamma..sub.2 is presented for an example (.DELTA..beta.=45.degree., .delta..sub.G =11.725.degree., .alpha.=-30.68.degree., .theta.=47.87.degree., .beta..sub.v =127.45.degree. or, respectively, t.sub.v =8:30) in FIG. 4. It can be recognized that at the two days of the annual times with the limiting solar declination angle .delta..sub.G just no solar ray can penetrate the prismatic pane and that the solar radiation blocking effect of the prismatic pane is vanishing more and more with a decreasing solar declination angle .delta.. As, of course, the radiation blocking effect of the prismatic pane holds for solar radiation as well as for radiation incident from the sky, the part of the sky radiation for which .gamma..sub.2 &gt;.kappa. holds cannot penetrate, too. Therefore, this prismatic pane offers the protection from solar radiation and the energetic advantages of the prismatic pane described in the French patent application no. 8017364 for a wide range of window directions and, moreover, enables the individual choice of the annual solar radiation blockade time by adequate dimensioning of the prismatic ribs. However, this prismatic pane offers no clear view, too, and is applicable for vertical windows only. In comparison to common glass panes also this prismatic pane offers better protection from glare of direct solar radiation at locations in the vicinity of a window, but does not achieve an improved daylighting of the deeper parts of a room. The manufacturing costs of the pane increase considerably, if a saw tooth profile turns out to be necessary.
Panes with Horizontal Incisions or Cavities
Moreover a pane for vertical windows the optical effective part of which consists of horizontal ribs vertically positioned one above another is known (Edmonds I. R., 1993. Performance of laser cut light deflecting panels in daylighting applications. Solar Energy Materials and Solar Cells 29, 1-26). This system can be manufactured, for instance, from acrylic glass panes in which narrow, parallel grooves--possibly employing Laser beams--have been cut. (FIG. 5). The cross-sections of these ribs can have the shape of a rectangle or of a parallelogram not essentially deviating from a rectangle with an aspect ratio h/b.
After intruding into a rib a ray will leave the rib again at the rear face after none, one or more reflections depending on the point of impact, the angle .eta. of the ray, the aspect ratio h/b and the shape of the rib cross-section. FIG. 6 presents an example of three possible ray traces within the cross-sectional plane of the rib for three different angles .eta.. It can be recognized that a part of the rays--depending on the angle .eta.--receives a new, ascending direction, whereas the remaining part of the rays keep their former direction. Actually the part of the rays with new, ascending direction varies in dependence on the direction of the impinging radiation from 0 to 1; this holds too, if the cross-sectional plane of the rib is a parallelogram. In spite of the directional dependency of the ray directing function this system directs a considerable part of the radiation incident from a clear or overcast sky on ascending traces against the usually white ceiling of a room and improves the daylighting of deep rooms in this way. However, direct solar radiation which, of course, at a discrete daytime is incident just from one direction will generate--depending on daytime and annual time--very different and quickly varying daylighting situations and ray directions in rooms equipped with this pane system and disturbing glare effects will occur. Therefore, this system--even with an adequate coating--is not qualified as pane protecting from solar radiation and it offers--in comparison to common glass panes--no capability to control the heat irradiation in summer and in winter. For vertical windows, however, which are essentially directed to the north--on the southern hemisphere: to the south--this system which also permits an acceptable clear view is qualified for the improved daylighting of deep rooms. At application locations in the vicinity of the equator this system applied as a pyramidal ceiling daylight aperture in comparison to a corresponding ceiling daylight aperture with common glass panes is as well capable to effectively reduce the heat irradiation into a room as to improve the daylighting of a room.
Panes with Horizontal, Specular Profile Bars
The German patent application DE A1 E04D003-35 describes a pane which uses horizontal, specular profile bars in the intermediate space between the two panes of a pane system (FIG. 7) in order to reject direct solar radiation during summer time and to transmit direct solar radiation--directed into ascending directions--into the room during winter time. Correspondingly the radiation incident from the overcast or clear sky with low to mean declination angles is transmitted into the room, whereas the radiation incident from the overcast or clear sky with mean to high declination angles is rejected. This pane, therefore, has the aim to control the heat irradiation in such a manner that in summer as little energy as possible and in winter as much energy as possible can intrude into the room, and--in comparison to common panes--to accomplish an improved daylighting of deep rooms by directing the incident light against the usually white room ceilings. With the aid of the RADIANCE computer program this system has been simulated for a test room with a window directed to the south (Moeck M., 1998. On daylight quality and quantity and its application to advanced daylight systems. Journal of the Illuminating Engineering Society Winter 1998, 3-21) and, moreover, has been experimentally investigated tigated (Aizlewood M. E., 1993. Innovative Daylighting Systems: An experimental evaluation. Lighting Research and Technology 25, 141-152) and has been compared to other systems. It was found that this system--disregarding potential glare effects--can provide the required protection from solar radiation and can contribute to the equalization of daylighting in deep rooms. But as this system does not only strongly reduce the intrusion of light and energy in summer but also in winter, for each application it has to be estimated, if this system performs the required energy effect. To a certain extent this system provides a clear view. As the profile bars, however, require a larger part of the clear window area than the segments of a common Venetian blind, the clear view provided by this system is less than that provided by a window with a common Venetian blind. Because of the exclusively horizontally aligned profile bars this system as well as the already discussed prismatic pane corresponding to the French patent application no. 8017364 is suited for windows essentially directed to the south only. If the sky is clear and there is direct solar radiation, glare effects changing with daytime from the specular reflecting profile bars have to be expected.
Solar Radiation and Light Control Systems for Vertical Windows
Furthermore a non-movable prismatic pane system (FIG. 8) is known (Bartenbach, C., 1986. Neue Tageslichtkonzepte. Technik am Bau 4, Germany) which consists of two prismatic panes and one interior mirror. Both prismatic panes and the interior mirror are built together such that they form a space with an isosceles cross-section. The prismatic pane protruding to the outside is to reflect the direct solar radiation which can impinge up to a maximum solar elevation angle and to transmit the intensive radiation from the zenith range of the sky to the interior mirror. The transmitted radiation is directed by the interior mirror to the second prismatic pane which has the task to direct the radiation upward against the white ceiling of the room and, thus, to generate--as far as possible--a uniform, non-blinding daylighting of deep rooms. In order to be able to fulfil this task one face of the prismatic ribs of each of these panes is coated with an evaporated, specular reflecting layer of aluminum. This system, too, was analyzed with the aid of the computer program RADIANCE for a test room with a window directed to the south (Moeck M., 1998. On daylight quality and quantity and its application to advanced daylight systems. Journal of the Illuminating Engineering Society Winter 1998, 3-21). It was found out that this system can provide the required, nearly perfect protection from solar radiation and that it avoids glare effects from direct solar light. But obviously it does not contribute to equalize the daylighting of deep rooms. As well in summer as in winter it essentially reduces the light and energy input into rooms, so that this system works rather uniformly in summer and in winter--i.e. without a significant, seasonal dependent control effect--as a light and energy dimming system. This system does not provide a clear view. Therefore and because of the externally protruding prismatic pane it is mainly suited as a skylight in combination with a common, clear-view, solar radiation restraining pane arranged below of it. Because of the exclusively horizontally aligned prismatic ribs this system as well as the systems already described above is suited for windows essentially directed to the south only.
Two further systems (Ruck N. G.,1985. Beaming daylight into deep rooms. Building Res. Pract. 6, 144-147 and, respectively, Beltran L. O., Lee E. S., Selkowitz S. E., 1997. Advanced optical daylighting systems: Light shelves and light pipes. Journal of the Illuminating Engineering Society Winter 1997, 91-106) have been designed which--similar to the system of Bartenbach described herein--have the task to direct daylight with an upper, vertical window part--called skylight--into the deeper ranges of rooms, in particular against the ceiling. In contrary to the system of Bartenbach these systems, however, aim for the use of the direct solar light for the daylighting of rooms; they are rather complex and expensive and contain parts which protrude beyond the vertical facades of buildings. Systems of this kind, therefore, have a strong influence on the facade of a building and thus restrict the creative design of architects.
Two Vertical Panes with Engaged, Horizontal Prismatic Ribs
Furthermore there is known a system (European patent application 833 01687.6, publication 0092322 A1) which consists of two panes with horizontal prismatic ribs (FIG. 9). The prismatic ribs of both panes all of which have identical cross-sections in the shape of a rectangular triangle are facing each other and are engaged such that just a small gap remains between both of the panes. The so-called "characteristical" cross-section of the prismatic ribs is determined by the basic prism angle .theta. and the faces C.sub.A, f.sub.A and S.sub.A (FIG. 10). The characteristical cross-section of the prismatic ribs can be employed as a substitute of the actual configuration for the investigation of ray traces, as the parallel shift of the front face a.sub.A causes just an insignificant parallel shift of the ray trace. The blockade effect of the system for rays within the cross-sectional plane holds for the range between the limiting angles EQU .eta..sub.Go =arcsin[n.multidot.sin(.theta.-.kappa.)] (10)
and EQU .eta..sub.Gu =-arcsin[n.multidot.cos(.theta.+.kappa.)], (11)
as far as the rays intrude into the characteristical cross-section within a certain range indicated by the partial face C.sub.R in FIG. 10. A major part of the radiation, however, intrudes beyond of this range into the characteristical cross-section, is reflected at the rear face f.sub.A, impinges again on the front face a.sub.A --in FIG. 10 substituted by the face c.sub.A --and is reflected thereon and impinges by such a steep incident angle on the rear face s.sub.A that this face is penetrated by the radiation. If little reflection losses at the faces are neglected, the ratio of the reflected radiation and the total radiation which is incident on the face c.sub.A with an angle .eta. within the range .eta..sub.Go &gt;.eta.&gt;.eta..sub.Gu is EQU C.sub.R /C.sub.A =2.multidot.cos(.theta.-.eta..sub.1).multidot.cos.theta./cos.eta..sub.1 (12)
The ratio of the transmitted radiation and the total incident radiation 1-C.sub.R /C.sub.A for .theta.=76.degree. in dependence on the angle .eta..sub.1 is presented in FIG. 11. It can be recognized that radiation with angles from .eta..sub.1 =0.degree. to .eta..sub.1Gu =27.8.degree. can penetrate completely; within this angular range the system provides a clear view. Radiation with angles from .eta..sub.1Go =34.17.degree. to .eta..sub.1 =41.81.degree. can--disregarding reflection losses--penetrate completely as well, but the system does not provide a clear view within this angular range. Within the angular range 27.8.degree.&lt;.eta..sub.1 &lt;34.17.degree., however, more than half of the radiation penetrates. In opposition to the systems already described this system thus has the advantage that it provides a clear view within the lower angular ranges, but the disadvantage that the radiation within the mean and the upper angular ranges is not satisfactorily or not at all reflected. Therefore, the effect protecting from solar radiation of this system is insufficient. In the international patent application PCT/GB94/00949, publication WO 94/25792, a similar system is described.